A lot of basic stuff seems to be missing / under-developed for natural language processing in the Indonesian language ?? Following are some links that I found and might be useful:
- My fork of Peb Ruswono Aryan's github repo, containing his implementation of a HMM-based POS tagger (originally decribed in this paper).
- Links to a whole bunch of training corpuses, including another POS tagger implementation in Java.
- Wikipedia in Indonesian language, might be useful for parallel training with the English version.
For sentiment analysis, due to the lack of training corpuses, unsupervised/semi-supervised approaches might be the way to go.  presents Latent Sentiment Model, a special case of the standard LDA with 3 topics only: positive, negative, neutral, and uses this for sentiment analysis on Chinese text. Results seem to be pretty decent .. Might have a play with implementing it later.
 He, Yulan. "Latent sentiment model for weakly-supervised cross-lingual sentiment classification." Advances in Information Retrieval. Springer Berlin Heidelberg, 2011. 214-225.